G.D.Birkhoff introduced a mathematical billiard inside of a convex domain as the motion

of a massless particle with elastic reflection at the boundary. A theorem of Poncelet says

that the billiard inside an ellipse is integrable, in the sense that the neighborhood of the

boundary is foliated by smooth closed curves and each billiard orbit near the boundary

is tangent to one and only one such curve (in this particular case, a confocal ellipse).

A famous conjecture by Birkhoff claims that ellipses are the only domains with this

property. We show a local version of this conjecture - namely, that a small perturbation

of an ellipse has this property only if it is itself an ellipse. It turns out that the method

of proof gives an insight into deformational spectral rigidity of planar axis symmetric

domains and gives a partial answer to a question of P. Sarnak.

This is based on several papers with Avila, De Simoi, G.Huang, Sorrentino, Q. Wei.

The talk will be accessible to a general audience.

of a massless particle with elastic reflection at the boundary. A theorem of Poncelet says

that the billiard inside an ellipse is integrable, in the sense that the neighborhood of the

boundary is foliated by smooth closed curves and each billiard orbit near the boundary

is tangent to one and only one such curve (in this particular case, a confocal ellipse).

A famous conjecture by Birkhoff claims that ellipses are the only domains with this

property. We show a local version of this conjecture - namely, that a small perturbation

of an ellipse has this property only if it is itself an ellipse. It turns out that the method

of proof gives an insight into deformational spectral rigidity of planar axis symmetric

domains and gives a partial answer to a question of P. Sarnak.

This is based on several papers with Avila, De Simoi, G.Huang, Sorrentino, Q. Wei.

The talk will be accessible to a general audience.

## Date:

Thu, 08/06/2017 - 14:30 to 15:30

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem